Hensel's Lemma and Field Theory

Related lectures (32)

Explores transcendence degree in algebraic fields and classical analytic functions.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores p-adic expansion, unique representations, and power series for computing p-adic expansions.

Covers the Gauss-Wantzel Theorem and Fermat prime numbers.

Explores the definition of Q_p and the completion of Q,1(p) to form Qp.

Explores ramification theory, residue fields, Galois extensions, and decomposition groups in algebraic number theory.

Introduces Galois fields, elliptic curves, factorization algorithms, and the discrete logarithm problem in cryptography.

Covers the completion of a field, focusing on algebraic closure and function convergence.

Covers homomorphisms, algebraic extensions, cutting, splitting, and separable elements in Fok [x].

Covers the properties of finite dimensional algebras and non-semisimple representations.

Covers the study of projective varieties and their relation to compact manifolds.

Examines conditions for the existence of invertible matrices satisfying specific matrix equations involving eigenvalues.

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